Plane Curve Bibliography

The following is a list of references from math journals i know about. This list is made in 1995.

Cayley, Arthur, “On the classification of cubic curves” Trans. Camb. Phil. Soc. XI (1866) 81-128.
Besant, W.H., Roulettes and Glissettes, London (1870).
Salmon, George, Lessons in Higher Algebra, Dublin (1876).
Proctor, R.A., The Geometry of Cycloids (1878).
Salmon, George, Higher Plane Curves, Dublin (1879); reprinted by Chelsea Pub. Co. 1960.
Salmon, George, and O.W. Fiedler, Analytische Geometrie der höheren ebenen Kurven, Leipzig (1882).
Casey, J., A Treatise on the Analytic Geometry of the Point, Line, Circle, and Conic Section, London (1883).
Schroeter, Heinrich, Theorie der ebenen Kurven, Leipzig (1888).
Brocard, H., “Le trifolium” Mathesis (2) vol. 2 (1892), suppl. II.
Frost, P., Curve Tracing, Macmillan (1892); reprinted by Chelsea Pub. Co.
Basset, A.B., Elementary Treatise on Cubic and Quadric Curves (1901).

Converse, H.A., “On a system of hypocycloids” Annals of Math. (2) 5 (1903-03) 105-139.

Grace, J.H., and A. Young, Algebra of Invariants, Cambridge (1903).
Texeira, F. Gomes, Traité des courbes spéciales remarqueables planes et gauches (1908-15).
Wieleitner, H., Spezielle ebene Kurven, Leipzig (1908).
Lefschetz, S., “On the existence of loci with given singularities” Trans. Amer. Math. Soc. 14 (1913) 23-41.

Ganguli, Surendramohan, The Theory of Plane Curves, Univ. of Calcutta (1925).
Hollcroft, T.R., “Multiple points of algebraic curves” AMS Bulletin 35 (1929) 841-849.
Coolidge, J.L., Treatise on Algebraic Plane Curves, Oxford (1931); reprinted by Dover (1959).
Hilton, Harold, Plane Algebraic Curves, Oxford (1932).
Weaver, J.H., “On the cubic of Tschirnhausen” Nat. Math. Mag. 16 (1942) 371-374.
Bilo, J., “Remarkable cubic curves in metrically special homaloidal nets” [Dutch] Simon Stevin 25 (1947) 59-82.
Bosteels, G., “The scyphoid, a rational quartic curve” [Dutch] Nieuw. Tijdschr. Wiskunda 35 (1947) 121-125.
Lilley, S., “On the construction of algebraic curve branches of given composition” J. London Math. Soc. 22 (1947) 67-74.
Godeaux, Lucien, Géométrie Algébrique, Sciences et Lettres, Liége (1949).
Semple, J.G., and L. Roth, Introduction to Algebraic Geometry, Oxford (1949).
Edge, W.L., “A plane quartic with eight undulations”, Proc. Edinburgh Math. Soc. 2 (1950) 147-162.
Edge, W.L., “A plane quartic curve with twelve undulations” Edinburgh Math. Notes 35 (1954) 10-13.
Ganát, Ludêk, and Miroslav Fiedler, “Rational curves with a maximum number of nodes” [Czech] Casopis Pest. Mat. 79 (1954) 157-161.
Primrose, E.J.F., “Coincidence points of a curve”, Tôhoku Math. J. 2 (1954) 35-37.
Primrose, E.J.F., “A property of quartic curves with two cusps and one node” Edinburgh Math. Notes 39 (1954) 1-3.
Northcott, D.G., “A note on the genus formula for plane curves” J. London Math. Soc. 30 (1955) 376-382.
Primrose, E.J.F., Plane Algebraic Curves, New York (1955).
Bernhart, Arthur, “Curves of pursuit - II” Scripta Math. 23 (1958) 49-65.
Blum, Richard, “On a pointwise construction of the lemniscate” Canadian Math. Bull. 1 (1958) 1-4.
Baker, Henry F., Principles of Geometry. Vol. 5: Analytic Principles of the Theory of Curves, New York (1960).
Spain, Barry, Analytical Quadrics, New York (1960).

Zwikker, C.; The Advanced Geometry of Plane Curves and their Applications; Dover Publications, N.Y.; 1963;

Jeffrey, A., “On the determination of the envelope of a family of epitrochoids with applications” SIAM J. Applied Math. 14 (1966) 502-510.
“Curves” and “Special Curves” Encyclopedia Britannica.

C.B.Boyer; Historical Stages in the Definition of Curves; National Mathematics Magazine. XIX (1944-5) 294-310. (recommended by Robert C Yates in his preface.)

George E. Martin; Transformation Geometry, An Introduction to Symmetry, Springer-Verlag, New York 1982.


Conic Sections

B. Bridge, Treatise on the Construction, Properties, and Analogies of the Three Conic Sections (from the 2nd London edition), jointly published by Durrie and Peck, New Haven and Collins, Keese, and Co., New York, 1839.

Martin Gardner; Penrose Tiles to Trapdoor Ciphers; W.H.Freeman and Co.; 1989. Chapter 15.

David Hilbert and S. Cohn-Vossen; Geometry and the Imagination; Chelsea; 1952; Chapter 1.

H.S.M. Coxeter; The Real Projective Plane; Springer-Verlag; 1993; Chapter 6-7.

Lee. Whitt; The standup conic presents: the parabola and applications; UMAP Journal (The Jounal of Undergraduate Math and its applications) 3 (1982); p.285-313.
Lee. Whitt; The standup conic presents: the ellipse and applications; UMAP Journal 4 (1983); p.157-183.
Lee. Whitt; The standup conic presents: the hyperbola and applications; UMAP Journal 5 (1984); p.9-21.

These are great articles on conic sections. Not mathematical. It describe a multitude of applications of conic sections, many of which are not well-known. Most interesting read.


Mathematics Magazine (Published by Mathematical Association of America)

v.50. 1977. p.87-89.
Rotary engine geometry.
David H. Nash.
(Possible keyword: trochoid, cycloid, hypotrochoid, hypocycloid, epicycloid)

v.60, No.3. June 1987. p.131-140.
Curves of Constant Width from a Linear Viewpoint.
J. Chris Fisher.
Lots reference. I have the article.

v.60, No.3. June 1987. p.167-168.
Reflections on the Ellipse
William C. Schulz; Charles G. Moore
A proof on the reflection property of ellipse.
I have the article. Have not read it yet.

v.65, No.3. June 1992. p.147.
Reflection Properties of Curves and Surfaces.
Daniel Drucker
Proof that conic sections and surface of revolutions of such are the only curve and surfaces with reflection property.
20 references.

The Mathematical Gazette
(The Journal of the Mathematical Association)

v.13 1926. p.232-235
The asymptotes of plane curves

v.13 1926. p.97-103

v.15 1930. p.486-487
The polar equations of a curve

v.15 1930. 22
The involute of the astroid

v.15 1930. 436
The curve of pursuit

v.18 1934. p.258-266
The tracing of cubic curves

v.21 1937. 418
Note on the three-cusped hypocycloid

v.23 1939. 92
On the three-cusped hypocycloid

v.25 1941. p.165-167
Repeating curves

v.25 1941. p.12-15
The cissoid of Diocles

v.26 1942. 214
The inflexions of a plane cubic

v.27 1943. p.4-12
On some general ovals of Cassinian type

v.27 1943. p.194-197
Real quadrics and the circle at infinity

v.29 1945. p.66-67
On the three-cusped hypocycloid

v.29 1945. p.219-220
The limacon and the cardioid

v.30 1946. p.145-146
On the three-cusped hypocycloid

v.36 1952. p.51-53
The Cartesian oval

v.36 1952. p.207-208
On a special type of plane trinodal quartic curve

v.37 1953. p.256-260
The curve of pursuit

v.40, No.331. Feb. 1956. p.1-4
Curves of Pursuit.
Very much application on military of fighter plane persuing a bomber.

v.40, No.331. Feb. 1956. p.11
The Power of a Point for a Curve.
Too mathematical, on algebraic curves.

v.41, No.336. May 1957. p.102-105
The Cissoid of Diocles.
(copy made)

v.41, No.338. Dec.1957. p.254-257
Negative Pedal of the Ellipse with Respect to a Focus.
(copy made)

v.43, No.343. Feb. 1959. p.34.
Pursuit Curves and Mathematical Art.
A very short (two paragraphes) note on how some doodle using the idea of envelope of lines could be drawn to form a beautiful wallpaper design. No mathematics discussed.
(copy made)

American Mathematical Monthly

v.8 1901. p.241.
Certain hyperbolic curves of the nth order

v.13 1906 p.221-226.
On a certain class of curves given by transcendental equations

v.14 1907. p.52.
On a certain quartic curve which may degenerate into an ellipse

v.15 1908. p.7.
On a certain class of quartic curves

v.24. 1917. p.213-220.
On the construction of certain curves given in polar coordinates

v.25. 1918. p.223-225.
Relating to Generalizations of the Witch and the Cissoid
Frederick H. Hodge.
(copy made)

v.25. 1918. p.189-193.
The Logarithmic Spiral.
copy made. I have not read it.

v.25. 1918. p.276-282.
Euler Integrals and Euler Spiral-Sometimes called Fresnel Integrals and the ClothoÏde or Cornu's Spiral.
copy made. I have not read it.

v.26. 1919. p.21-32.
Concerning a new method of tracing cardioids
William F. Rigge

v.26 1919. p.151-154.
The existence of cusps on the evolute at points of maximum and minimum curvature on the base curve

v.26. 1919. p.332-340.
Cuspidal Rossettes
William F. Rigge

v.27. 1920. p.151-157.
Envelope Rosettes
William F. Rigge

v.27 1920. p.398-401
The danger area curve

v.28 1921. p.54-61
A curve of pursuit

v.29. 1922. p.6-8.
Cuspidal Envelope Rosettes
William F. Rigge

v.31 1924. p.71-77
The three bar curve

v.31 1924. p.222-227
The cochlioid

v.33 1926. p.273-274
La courbe du diable

v.34 1927. p.426-429
A simple way to discuss points of inflection on plane cubic curves

v.34 1927. p.262-263
The devil's curve again

v.39 1932. p.409-412
Cycloidal curves

v.40 1933. p.596-598
An unusual spiral

v.44 1937. p.167-168
The quadratrix and the associated cochleoid

v.46 1939. p.85-86
The deltoid regarded as the envelope of Simson lines

v.47 1940. p.11-18
The triangle; its deltoids and foliates

v.52 1945. p.384-387
Some properties of the limacon and cardioid

v.55 1948. p.7-14
An anallagmatic cubic

v.56 1949. p.165
Note on quartic curves

v.61. 1954. p.381.
G.B. Robinson

v.64. No.5. 1957. p.333.
Curves with a Kind of Constant Width.
Paul J. Kelly.
Mathematical treatment related to pedal curves. Makes a interesting read.

v.64. No.5. May 1957. p.359-361.
The Names of the Curve Agnesi
T.F.Mulcrone, S.J.
(copy made)

v.64 1957. p.362-364
On degenerate conics
J.W.Lasley, Jr.
(copy made)

v.75. No.1. Jan. 1968.
The Problem of Apollonius.

v.75. No.4. April. 1968.
Classroom Notes: The Optical Property of the Conics.
Harley Flanders.
A half page article that proves optical property of conics by vectors. 

v.87. No.4. April.1980. p.295.
Classroom notes: On the Reflective Property of Ellipses
A non-calculus proof and a argument using force/energy concepts.

v.102. No.9. November 1995. p.771.
My Favorite Elliptic Curve: A Tale of Two Types of Triangles
Richard K. Guy. 

v.102. No.9. November 1995. p.782.
Stalking the Wild Ellipse
Keith M. Kendig

v.102. No.9. November 1995. p.831.
The Evolution of Elliptic Curves
John Stillwell

The College Mathematics Journal

v.23. 1992. p.20-35.
Trochoids, Roses, and Thorns--Beyond the Spirograph.
Leon M. Hall
12 references.
Copy made. Have not read yet.

v.24. No.5. November 1993. p.422-430.
Two Trisectrices for the Price of One Rolling Circle
Jack Eidswick
Copy Made. Have not read yet.
Key words: trisectrix of Maclaurin

Scripta Mathematica

v.23. Memorial Issue, 1957. Nos.1-4.p.49
Curves of Pursuit II.
Arthur Bernhart.
A mathematical treatment, but I think accesible to undergraduate.

v.23. Memorial Issue, 1957. Nos.1-4.p.49
Miscellaneous Notes: Conic Sections in Perspective.
Ali R. Amir-Moéz.
(copy made)

Ann. Math.

v.30 1928. p.52-60
Canonical forms of plane cubic curves

v.31 1930 p.629-632
Matrix conditions for multiple points of a ternary cubic

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